Question

If A = 3x2 + 2xy - 9y2 and B = 5x2 - 7y2 then find i)A+B ii) A - B iii) A* B

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Answer 1

Step-by-step explanation:

Given:-

A = 3x^2 + 2xy - 9y^2

and

B = 5x^2 - 7y^2

To find:-

Find the following :

i)A+B

ii) A - B

iii) A×B

Solution:-

Given that

A = 3x^2 + 2xy - 9y^2

and

B = 5x^2 - 7y^2

Now ,

i) A + B

=> (3x^2 + 2xy - 9y^2)+(5x^2 - 7y^2)

=> (3x^2+5x^2)+2xy+(-9y^2-7y^2)

=> 8x^2+2xy-16y^2

(or)

3x^2 + 2xy - 9y^2

5x^2 -7y^2

(+)

______________

8x^2 +2xy-16y^2

_______________

ii) A - B

=> (3x^2 + 2xy - 9y^2) - (5x^2 - 7y^2)

=> 3x^2+2xy-9y^2-5x^2+7y^2

=> (3x^2-5x^2)+2xy+(-9y^2+7y^2)

=> -2x^2+2xy-2y^2

(or)

3x^2 + 2xy - 9y^2

5x^2 -7y^2

(-)

_______________

-2x^2+2xy-2y^2

_______________

iii)A×B

=> (3x^2 + 2xy - 9y^2) × (5x^2 - 7y^2)

=> 3x^2(5x^2-7y^2)+2xy(5x^2 - 7y^2)-9y^2(5x^2 - 7y^2)

=> 15x^4 -21x^2y^2 +10x^3y-14xy^3 -45x^2y^2 +63y^4

=> 15x^4+(-21x^2y^2-45x^2y^2)+10x^3y-14xy^3 + 63 y^4

=> 15x^4 -66x^2y^2+10x^3y-14xy^3+63y^4

Answer:-

i)A+B=8x^2 +2xy-16y^2

ii) A-B = -2x^2+2xy-2y^2

iii)A×B = 15x^4 -66x^2y^2+10x^3y-14xy^3+63y^4